1. Field of the Invention
The present invention relates to an optical scanning apparatus, and more particularly to an optical scanning apparatus comprising a scanning optical system which employs a rotationally asymmetric aspheric surface and is suitable for a laser printer that is used as a computer output peripheral or an office information processing apparatus. The present invention further relates to a rotationally asymmetric aspheric scanning lens that is used for the optical scanning apparatus.
2. Description of the Prior Art
In laser printers, a structure has been employed which is arranged such that the laser beam is deflected to scan a photosensitive drum by the combination of an F.theta. lens and a rotating polygonal mirror. One of the problems that is encountered in scanning the laser beam is that scanning pitch errors are generated due to a tilt of reflective surfaces of the rotating polygonal mirror.
In order to obviate this problem, there have been proposed various methods for reducing adverse affects due to the tilt error of the rotating polygonal mirror by means of the combination of a cylindrical lens and a toric F.theta. lens (see Japanese Patent Unexamined Publication No. 48-98844), the combination of a prism and an F.theta. lens (see Japanese Patent Examined Publication No. 59-9883), the combination of a toric lens and an F.theta. lens (see Japanese Patent Unexamined Publication No. 48-49315) and the like. However, these methods suffer from difficulties in which an increased number of components must be used due to the use of two kinds of optical elements such as an asymmetrical optical element and an F.theta. lens as described above. In order to overcome these difficulties, it has also been proposed to impart the function of compensating for scanning pitch errors due to the tilt of the polygonal mirror in the F.theta. lens (see Japanese Patent Unexamined Publication No. 57-144515). An F.theta. lens of the type according to this proposal is provided with a cylindrical surface or a toric surface as well as ordinary spherical surfaces or planar surfaces. Assuming that a first plane is perpendicular to a second plane, the "toric surface" means a surface having different radii of curvature in the first and second planes. Namely, the toric surface is expressed by the following secondary expansion equation: EQU z=Ax.sup.2 +By.sup.2 . . . (1)
where z corresponds to the optical axis, xz and yz correspond to the surfaces that are perpendicular to each other and that include the optical axis, and A and B are coefficients, in which A.noteq.B holds, and in which A and B are independent of the view angle .theta. relative to the optical axis.
In a laser scanning apparatus in which the above-described toric surface is employed, assuming that the optical scanning surface is xz, the surface which affects the surface tilt is yz, the main scanning direction is x, the sub-scanning direction is y, and the focal lengths within each of the surfaces are fx and fy, respectively, the following relationship holds: EQU fx.noteq.fy, and fx&gt;fy . . . (2)
In particular, the focusing properties in the surface-tilt direction (sub-scanning direction) can deteriorate as can be clearly seen from the above-described formula. The reason for this lies in that the region that can be scanned by fx is limited since fx&gt;fy, causing excellent focusing properties to be prevented from being satisfied. The reason for the deterioration in the focusing properties in the sub-scanning direction resides in a field curvature aberration that is generated in the surface (surface yz) relating to the surface tilt. That is, the wave aberration at a specific view angle .theta. becomes as follows: EQU W=cy.sup.2 . . . (3)
where c corresponds to a coefficient. On the other hand, the focusing properties in the main scanning direction can be kept in a good condition when .theta. is 40.degree. or less. That is, an aberration is generated only in the surface tilt compensation direction (the direction of y-axis and sub-scanning direction) since W is brought to a non-functional relationship with x. Since c corresponds to a coefficient determined by the curvature radius, interval between lenses, refraction factor, view angle and the like, it cannot become zero due to a deterioration in the focusing properties if the contour of the lens surface is as such expressed by Equation (1). Another problem arises in that the alignment adjustment by means of rotating of the lenses is difficult to conduct since a plurality of aspheric surfaces are provided in the f.theta. lens.
To this end, the inventors of the present invention have proposed (Japanese Patent Unexamined Publication No. 62-265615 or U.S. Ser. No. 179,407) a structure arranged such that the number of the aspheric surfaces of the scanning lens (f.theta. lens) is decreased to one and the shape of this aspheric surface is arranged to be that as expressed by the following equation: ##EQU1## wherein a coefficient B' is a function of a scanning view angle .theta., and the curvature radius of the f.theta. lens in the surface tilt direction is changed in correspondence with the deflection direction. According to this proposal, the coefficient of the term y.sup.2 of the wave aberration W can be brought to come closer to 0 by arranging the curvature radius in the surface tilt direction (sub-scanning direction) to become larger with the distance from the optical axis (axis z) as shown in dashed line .circle.B . This means that the focal distance fy in the sub-scanning direction is a function of the view angle .theta. so that fy is also changed in correspondence with the change in the view angle .theta.. In this proposal, the change in the curvature radius in the sub-scanning direction is symmetric with respect to the optical axis. Referring to FIG. 2, z-axis corresponds to the direction of the optical axis, while the yz surface is the surface that affects the surface tilt. Referring to this drawing, a continuous line .circle.A represents a conventional toric surface expressed by the following equation: EQU z=By.sup.2 +M . . . (5)
Thus, the focusing position can be brought to any position on the surface of the photosensitive drum by arranging the curvature radius in the sub-scanning direction to become larger with the distance from the optical axis as designated by the dashed line and by making the curvature radius outside the axis (.theta..noteq.0) larger than that in the surface tilt direction on the optical axis (.theta.=0) so as to be an aspheric surface .circle.B . Furthermore, the thus-arranged curvature radius is, together with the view angle .theta., monotone-increased bisymmetrically.